I've lived in Abu Dhabi for the last year. Many people will just fly from Dubai/ to Dubai if either there is no nonstop from AUH or if it's cheaper from DXB. You can do a cab or an Uber. most destinations are no more than 300 Dirhams, but Dubai cabs tend to be more expensive than Abu Dhabi cabs. Still, this is the best way to do it. Don't even think of trying to fly between the two.